论文标题
在不同的借贷和储蓄率下，Markowitz的连续时间Markowitz的均值变化模型
Continuous-time Markowitz's mean-variance model under different borrowing and saving rates
论文作者
论文摘要
我们研究了Markowitz在连续的黑色智商市场中的平均变异投资组合选择问题，并具有不同的借贷和储蓄率。相关的Hamilton-Jacobi-Bellman方程是完全非线性的。使用精致的部分微分方程和验证参数，该值函数被证明为$ c^{3,2} $平滑。还表明，有一个借贷边界和一个储蓄障碍，将整个贸易区域分为借款货币区域，一个储备区域以及按上升顺序的储蓄金属区域。最佳交易策略是连续时间策略（如大多数连续时间模型所建议的）和不连续的时间策略（如交易成本的模型所建议的）：一个人应该将她所有的财富都放在中间的全股区域中，并在其他两个地区不断以财富和时间的反馈形式将其交易。卖空股票绝不是最佳选择。还提供了数值示例，以验证理论结果并提供更多的财务见解。
We study Markowitz's mean-variance portfolio selection problem in a continuous-time Black-Scholes market with different borrowing and saving rates. The associated Hamilton-Jacobi-Bellman equation is fully nonlinear. Using a delicate partial differential equation and verification argument, the value function is proven to be $C^{3,2}$ smooth. It is also shown that there are a borrowing boundary and a saving barrier which divide the entire trading area into a borrowing-money region, an all-in-stock region, and a saving-money region in ascending order. The optimal trading strategy is a mixture of continuous-time strategy (as suggested by most continuous-time models) and discontinuous-time strategy (as suggested by models with transaction costs): one should put all her wealth in the stock in the middle all-in-stock region, and continuously trade it in the other two regions in a feedback form of wealth and time. It is never optimal to short sale the stock. Numerical examples are also presented to verify the theoretical results and to give more financial insights beyond them.
